Metonic Cycle

Lunisolar calendars have twelve lunar cycles in their common years. That’s about eleven days short of a solar year. Each month starts on the day of a new moon, or on the day a new lunar crescent is first sighted. Without intercalation, months start eleven days later in relation to seasons each successive year.

Metonic Cycle

The Metonic Cycle is a period of about 6939.6 days, the approximate length of both 235 consecutive lunations and 19 solar years. Knowledge of this cycle is important in determining when to assign intercalary months to lunisolar calendars.
Meton, an Athenian who lived in the middle of the fifth century B.C., is the cycle’s namesake. Meton himself referred to it in a publication as the nineteen-year cycle. There is some question as to whether Meton discovered it on his own or whether he learned of it from Babylonian sources, because it was discovered there about fifty years before Meton’s time.

Lunisolar calendars will roughly keep in step with seasons if a thirteenth month is added to them in seven out of each 19 years. In order to do this almost perfectly, there should be an additional one-day correction after each 222 years.
The cycle was perhaps first used to determine frequency of intercalation of a thirteenth month in the Greek Calendar, which consisted of 12 lunar months (a total of 354 days) 1 and intercalation of an extra month every second year just before the rule was applied.
As late as the twenty-five hundred years ago, official letters in Babylon informed local officials when the current year should include an intercalary month. 2 It wasn’t until about 380 B.C. that Babylonian calendar authorities regularly applied a one month intercalation in years 3, 6, 8, 11, 14, 17, and 19 of each cycle.
Geminus pointed out that: “It is a matter of indifference if, while preserving the same disposition of intercalary months, you put them in other years.”
The Metonic cycle was improved by Hipparchus and Callipus of Cyzius (c. 370-300 BC). Calippus formed what has been called the Callippic period, a cycle of four Metonic periods. Moon phases repeat on about the same ordinal day of each of these periods.
One of the most unexplainable things about the Metonic Cycle is that mankind has observed the sky for hundreds of thousands of years, 3 but this easily recognized period was not known until only about twenty-five hundred years ago, less than one-half of one percent of mankind’s time on earth.